According to Yoshida “When you buy a PS4 game on smartphone, it will wake your PS4 up to start downloading the game. PS4 goes back to sleep after that.”
In practice, this is useful for those who purchase pre-paid PSN cards in the store, allowing them to start the game downloading while driving home. It will also be beneficial to those who purchase games while on holiday, allowing them to come home to a console already ready to play.
This marks part of larger a shift towards a more user friendly form of downloadable content. Both the PS4 and Xbox One have made this ease of access one of their major priorities.
Previously, it was announced that any digital game on the PS4 could be played while still downloading. Following a short period where the base files from the game are installed on the system, the game will download additional content on a mission by mission basis.